Multistage median cascaded canceller

ABSTRACT

An adaptive signal processing system utilizes a a Multistage Weiner Filter having an analysis section and a synthesis section, which includes a main input channel for receiving a main input signal, an auxiliary input channel for receiving an auxiliary input signal, and a processor. The processor includes an algorithm for generating a data adaptive linear transformation, followed by computing an adaptive weighting w med  of the data, and then applying the computed adaptive weighting w med  to a function of the main input signal and the auxiliary input signal to generate an output signal. The system includes a plurality of building blocks arranged in a Gram-Schmidt cascaded canceller-type configuration for sequentially decorrelating input signals from each other to thereby yield a single filtered output signal. Each building block includes a local main input channel which receives a local main input signal, a local auxiliary input channel which receives a local auxiliary input signal, and a local output channel which sends a local filtered output signal. Each building block generates an adaptive weight w med  that preferably uses just the sample median value of the real part of a complex weight w med , with the imaginary part set to zero, of the ratio of local main input weight training data to local auxiliary input weight training data. Each building block generates a local output signal utilizing the adaptive weight w med . The effect of non-Gaussian noise contamination on the convergence MOE of the system is negligible. In addition, when desired signal components are included in weight training data they cause little loss of noise cancellation.

FIELD OF THE INVENTION

[0001] The invention relates in general to an adaptive signal processingsystem. More specifically, the invention relates to an adaptive signalprocessing system that utilizes a multistage median cascaded cancellerto formulate an efficient data transformation followed by thecalculation of adaptive weights and filter out undesired noise.

BACKGROUND OF THE INVENTION

[0002] Adaptive signal processing systems have many applicationsincluding radar reception, cellular telephones, communications systems,and biomedical imaging. Adaptive signal processing systems utilizeadaptive filtering to differentiate between the desired signal and thecombination of interference and noise, i.e. thermal or receiver noise.An adaptive filter is defined by four aspects: the type of signals beingprocessed, the structure that defines how the output signal of thefilter is computed from its input signal, the parameters within thisstructure that can be iteratively changed to alter the filter'sinput-output relationship, and the adaptive algorithm that describes howthe parameters are adjusted from one time instant to the next.

[0003] Common applications of adaptive signal processing include: anadaptive radar reception antenna array, an adaptive antenna array foradaptive communications, and adaptive sonar. In these systems, desiredsignal detection and estimation is hindered by noise and interference.Interference may be intentional jamming and or unintentional receivedradiation. Noise is usually described as ever present receiver thermalnoise, generally at a low power level. In these applications antennaarrays may change their multidimensional reception patternsautomatically in response to the signal environment in a way thatoptimizes the ratio of signal power to the combination of interferencepower plus noise power (abbreviated as SINR). The array pattern iseasily controlled by weighting the amplitude and phase of the signalfrom each element before combining (adding) the signals. In general,multidimensional samples may be collected, e.g. over antenna elements,over time, over polarization, etc., where each sample is a separateinput channel to the adaptive processor. Adaptive arrays are especiallyuseful to protect radar and communication systems from interference whenthe directions of the interference are unknown or changing whileattempting to receive a desired signal of known form. Adaptive arraysare capable of operating even when the antenna elements have arbitrarypatterns, polarizations, and spacings. This feature is especiallyadvantageous when an antenna array operates on an irregularly shapedsurface such as an aircraft or ship.

[0004] Adaptive signal processing systems are required to filter outundesirable interference and noise. Due to the lack of a prioriknowledge of an external environment, adaptive signal processing systemsrequire a certain amount of statistically independent weight trainingdata samples to effectively estimate the input noise and interferencestatistics.

[0005] “Ideal” weight training data has a Gaussian probabilitydistribution for both its real and imaginary baseband components.However, real-world weight training data may be contaminated byundesirable impulse noise outliers, resulting in a non-Gaussiandistribution of real and imaginary components.

[0006] The number of weight training data samples required for SINRperformance of the adaptive processor to be within 3 dB of the optimumon average is called the convergence measure of effectiveness (MOE) ofthe processor. A signal is stationary if its statistical probabilitydistribution is independent of time. For the pure statisticallystationary Gaussian noise case, the convergence MOE of the conventionalSample Matrix Inversion (SMI) adaptive linear technique can be attainedusing approximately 2N samples for adaptive weight estimation,regardless of the input noise covariance matrix, where N is the numberof degrees of freedom in the processor (i.e., the number of antennaelements or subarrays) for a spatially adaptive array processor, or N isthe number of space-time channels in a space-time adaptive processing(STAP) processor). Referred to as the SMI convergence MOE, convergencewithin 3 dB of the optimum using approximately 2N samples for adaptiveweight estimation has become a benchmark used to assess convergencerates of full rank adaptive processors. General information regardingSMI convergence MOE may be found in Reed, I. S., Mallet, J. D., Brennan,L. E., “Rapid Convergence Rate in Adaptive Arrays”, IEEE Trans.Aerospace and Electronic Systems, Vol. AES-10, No. 6, November, 1974,pp. 853-863, the disclosure of which is incorporated herein byreference.

[0007] Conventional sample matrix inversion (SMI) adaptive signalprocessing systems are capable of meeting this benchmark for the purestatistically stationary Gaussian noise case. If, however, the weighttraining data contains non-Gaussian noise outliers, the convergence MOEof the system increases to require an unworkably large number of weighttraining data samples. The performance degradation of the SMI algorithmin the presence of non-Gaussian distributions (outliers) can beattributed to the highly sensitive nature of input noise covariancematrix estimates to even small amounts of impulsive non-Gaussian noisethat may be corrupting the dominant Gaussian noise distribution. Generalinformation regarding the sensitivity of the SMI algorithm may be foundin Antonik, P. Schuman, H. Melvin, W., Wicks, M., “Implementation ofKnowledge-Based Control for Space-Time Adaptive Processing”, IEEE Radar97 Conference, Oct. 14-16, 1997, p. 478-482, the disclosure of which isincorporated herein by reference.

[0008] Thus, for contaminated weight training data, convergence rate mayslow significantly with conventional systems. Fast convergence rates areimportant for several practical reasons including limited amounts ofweight training data due to non-stationary interference andcomputational complexity involved in generating adaptive weights. Inother words, the time which elapses while a conventional system isacquiring weight training data and generating adaptive weights mayexceed the stationary component of a given non-stationary noiseenvironment, and an adaptive weight thus generated has become obsoleteprior to completion of its computation.

[0009] Most real world data does not have a purely Gaussian probabilitydistribution due to contamination by non-Gaussian outliers and/ordesired signal components. Conventional signal processors assume thatthe weight training data has a Gaussian distribution, and therefore theydo not perform as well as theory would predict when operating with realworld data. If weight training data contains desired signals that appearto be outliers, the performance is similarly degraded. In an effort tocompensate for these performance problems, conventional systems employsubjective data screening techniques to remove perceived outliers fromthe data prior to processing. However, subjective screening isundesirable because the process is ad-hoc in nature, requires many extraprocessing steps, and may even degrade system performance.

[0010] Optimal, reduced rank, adaptive processors are derived primarilyto combat the problem of non-stationary data conditions (i.e. low samplesupport) often encountered in general applications. However, they stillhave convergence MOE's that are degraded by outliers. For radarapplications, these provide better SINR output than full rank methods,typically through the use of localized training data to improvestatistical similarity with the range cell under test (CUT). Anexemplary system is described in U.S. patent application Ser. No.09/933,004, “System and Method For Adaptive Filtering”, Goldstein etal., incorporated herein by reference.

[0011] Also, full rank, robust, adaptive processor research has resultedin novel open loop processors capable of accommodating an amount ofnon-Gaussian/outlier contaminated and nonstationary data, while stillproducing an SMI-like convergence MOE. An exemplary system is describedin U.S. patent application Ser. No. 09/835,127, “Pseudo-Median CascadedCanceller”, Picciolo et al., incorporated herein by reference,hereinafter referred to as a median cascaded canceller.

[0012] Reduced rank processors have a convergence MOE typically on theorder of 2r, where r is the effective rank of the interferencecovariance matrix. Effective rank refers to that value of r which isassociated with the dominant eigenvalues of the interference and noisecovariance matrix. General information regarding “effective rank” andgeneral trends in the convergence trends MOE of reduced rank processorsmay be found in “Principal Components, Covariance Matrix Tapers, and theSubspace Leakage Problem”, J. R. Guerci and J. S. Bergin, IEEETransactions on Aerospace and Electronic Systems, Vol. 38, No. 1,January 2002.

[0013] Given the demonstrated capabilities of these processors, it wouldbe desirable to provide an adaptive signal processing system thatutilizes features of both these types of systems.

SUMMARY OF THE INVENTION

[0014] The present invention provides an adaptive signal processingsystem that utilizes an MWF filter in combination with a median cascadedcanceller to compute a non-adaptive data transformation, forming a mainchannel and a set of auxiliary channels, followed by a data adaptivetransformation and a set of adaptive weights to generate a filteredoutput signal. The effect of non-Gaussian non-stationary noisecontamination on the convergence MOE of the system is significantlyreduced. In addition, when desired signal components are included inweight training data they cause reduced deleterious effects on noisecancellation.

[0015] In a preferred embodiment, the system and method are directed toan adaptive signal processing system that includes an analysis sectionof a Multistage Weiner Filter (MWF), a modified synthesis section of theMWF, which includes a main input channel for receiving a global maininput signal, a set of global auxiliary input channels for receiving acorresponding set of auxiliary input signals, and a processor. Theglobal main and the global auxiliary channels may be formed by anon-adaptive linear transformation of the original data channels. Theprocessor includes an algorithm for generating a non-adaptive lineartransformation producing a global main channel and global auxiliarychannels, a data adaptive linear transformation, followed by an adaptiveweighting and subtraction of the auxiliary data channels from the globalmain channel. The system includes a plurality of building blocksarranged in a Gram-Schmidt cascaded canceller-type configuration forsequentially decorrelating input signals from each other to therebyyield a single filtered output signal. Each building block includes alocal main input channel which receives a local main input signal, alocal auxiliary input channel which receives a local auxiliary inputsignal, and a local output channel which sends a local filtered outputsignal. Each building block generates an adaptive weight that preferablyuses just the real parts of a set of complex values determined from theratios of the local main channel samples to the local auxiliary channelsamples, w_(med). Each building block generates a local output signalutilizing the adaptive weight.

[0016] The effect of non-Gaussian noise contamination on the convergenceMOE of the system is negligible. In addition, when desired signalcomponents are included in weight training data they cause little lossof noise cancellation.

[0017] It would advantageously adaptively process non-stationary dataconditions via reduced rank processing while also accommodating outliercontaminated weight training data, ideally producing a convergence MOEcomparable to the above referenced benchmark for reduced rankprocessers, and potentially reducing desired signal cancellation whenweight training data includes desired signal components.

[0018] Other advantages and features of the invention will becomeapparent from the following detailed description of the preferredembodiments and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0019]FIG. 1 is a schematic diagram of an MMCC according to theinvention.

[0020]FIG. 2 is a schematic diagram of an MMCC according to theinvention.

[0021]FIG. 3 is a schematic diagram of an MMCC according to theinvention.

[0022]FIG. 4 is a block diagram of a conventional sample matrixinversion processor shown as an equivalent Gram-Schmidt cascadedcanceller processor.

[0023]FIG. 5 is a single block of a conventional Gram-Schmidt cascadedcanceller processor.

[0024]FIG. 6 is a block diagram of a cascaded canceller processorcomponent of an MMCC according to the present invention.

[0025]FIG. 7 is a single building block of a cascaded cancellerprocessor component of an MMCC according to the present invention.

[0026]FIGS. 8a-b are graphs showing the adapted pattern produced by anMWF as in the prior art.

[0027]FIGS. 9a-b are graphs showing the adapted pattern produced by anMMCC according to the invention.

[0028]FIG. 10 is a graph as in FIG. 8(a) for an MWF having a differentconfiguration.

[0029]FIG. 11 is a graph is in FIG. 9(a) for an MMCC having a differentconfiguration in accordance with the invention.

[0030]FIGS. 12a-b show the clutter spectrum for measured airborne radardata illustrating the input statistics input to an MMCC according to theinvention.

[0031]FIGS. 13a-b are graphs as in FIGS. 8a-b for an MWF having adifferent configuration and having input data statistics as shown inFIGS. 12a-b.

[0032]FIGS. 14a-b are graphs as in FIGS. 9a-b for an MMCC having adifferent configuration and having input data statistics as shown inFIGS. 12a-b in accordance with the invention.

[0033]FIG. 15 is a comparison graph of a prior art system and an MMCCaccording to the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0034] Referring now to FIGS. 1-3, a Multistage Median Cascaded Filter(MMCC) 10 receives input data x(k). The x(k) data stream is applied to asteering vector s 12, where processing begins with non-adaptivecalculations. First, the data vectors are projected onto the steeringvector to form an initial estimate of the desired signal:

d ₀(k)=s ^(H) x(k).  (1)

[0035] For example, d₀(k) may be the output of a conventional beamformeror a matched filter. In general, d₀(k) contains interference that comesin through the sidelobes of s. To prepare for a statistical analysisthat will identify and subtract this interference, the rest of the datamay be isolated by writing

x ₀(k)=Bx(k),  (2)

[0036] where B is a “blocking matrix” 14 that finds the projection ofthe data x(k) orthogonal to s, i.e., the projection onto the nullspaceof s.

[0037] The projection operation in (2) is uniquely defined. However, theprojection can be accounted for in at least two ways. In earlierapproaches, the blocking matrix was rectangular to account for theresult being an N−1 dimensional vector (i.e., a vector with length N−1).The other possibility is to consider the square blocking matrix:

B=I−ss ^(H).

[0038] The square matrix accounts for the same projection, but theprojection may be viewed as a subtraction in the fixed perspective ofthe original N-dimensional coordinate system (i.e., where all vectorshave length N). The choice between these two blocking matrices isrelevant to the numerical efficiency realized in the present invention.By choosing the square blocking matrix in preferred embodiments of thepresent invention, we can re-write (2) as

x ₀(k)=[I−ss ^(H) ]x(k)=x(k)−sd ₀(k)

[0039] By accounting for the projection in preferred embodiments of thepresent invention with the subtraction in the preceding equation, thecomputational cost for a block is O(NK). This gives us a significantsavings over the matrix multiplication shown in (2), which would costO(N²K).

[0040] Given d₀(k) and x₀(k) as new inputs, the processing continueswith a recursion of adaptive stages. The index i identifies the adaptivestage number (where i=1 is the first adaptive stage, and so on). Tosupport stage i, the block-averaged correlation between the two inputsto that stage is calculated according to

r _(i−1) =<x _(i−1)(k)d* _(i−1)(k)>_(K).  (3)

[0041] Stage i will use this correlation in terms of the correlationmagnitude δ_(i) and the correlation direction vector h_(i) 16,

δ_(i) =∥r _(i−1)∥=(r _(i−1) ^(H) r _(i−1))^(1/2),  (4)

and h _(i) =r _(i−1) /∥r _(i−1)∥.  (5)

[0042] While the correlation direction vector can be calculated by usingblock averaging with uniform weighting over the block, other averagingtechniques known to those skilled in the art may be used, based on therequirement of the particular application (e.g., time constraints,accuracy requirements) and the availability of processing resources. Theprojections of the data along this direction and orthogonal to thisdirection can account for this projection as a subtraction,

d _(i)(k)=h _(i) ^(H) x _(i−1)(k)  (6)

and x _(i)(k)=[I−h _(i) h _(i) ^(H) ]x _(i−1)(k)=x _(i−1)(k)−h _(i) d_(i)(k).  (7)

[0043] It should be noted that Equations (6) and (7) pertain to FIG. 1in that these particularly apply to an embodiment of the invention thatemploys a square blocking matrix, such as is described in theabove-referenced U.S. Ser. No. 09/933,004. For other embodiments usingnon-square matrices, x_(i)(k)=B_(i)x_(i−1)(k) and Equation (6) apply inthat form but with different dimensions. Either method may be considereda specific implementation used to generate a Krylov subspacerepresentation of the original data, such as is described in The Theoryof Matrices, P. Lancaster and M. Tismenstsky, Academic Press (1985),incorporated herein by reference. Any other method used to generate sucha Krylov subspace representation of the data may be equivalentlysubstituted. In the follow-on synthesis stage of the present invention,median-based filtering (denoted by the use of w_(med) weights in FIGS. 1and 2) is then applied to the Krylov subspace. This recursive analysismay be terminated in several ways. If the block of data X has full rank,then the projections may continue until all the data is projected onto aset of orthogonal unit vectors [s, h₁, h₂, . . . , h_(N−1)]. Thisanalysis would use N−1 stages (because s accounted for one directionalready). Or, if the block of data X is not full rank (for example, ifK<N is intentionally selected), then the rank of the data will“underflow” in the analysis. In that case, x_(i)(k) would contain onlyzeros for the highest stages

[0044] Referring also now to FIG. 3, alternatively, the filtering may beintentionally truncated to some smaller number of stages s (where1≦s≦N−1). Once the analysis is finished, the initializationε_(S)(k)=d_(S)(k) begins the synthesis along the lower chain of FIG. 1from right to left.

[0045] The synthesis may be better understood by considering aconventional general adaptive array having a sidelobe canceller form anda conventional Gram-Schmidt cascaded canceller. The adaptiveimplementation of a conventional Gram-Schmidt cascaded cancellerprovides a cascaded set of operationally identical, two-input cancellerGram-Schmidt L₂ building blocks, as is well known in the art. Inaccordance with the MMCC of the present invention, these Gram-Schmidt L₂building blocks are replaced with new L_(med) building blocks. EachL_(med) building block generates an adaptive weight w_(med) that in oneform is a complex adaptive weight whose real and imaginary parts arefound, as is further described below, by taking the sample median valueof the ratio of local main input weight training data z to localauxiliary input weight training data x for the real and imaginary partsseparately, applies the computed weight to a function of a local maininput signal and a local auxiliary input signal, and generates afiltered output signal.

[0046] Theoretically, the L_(med) building blocks produce the sameoptimal weight as the Gram-Schmidt L₂ building blocks if the number ofsamples of training data is very large (K→∞), and the two inputs eachhave symmetric probability density functions about the mean for theirreal and imaginary components (an example is the Gaussian pdf). Inaddition, the convergence MOE of the median cascaded canceller offers asignificant improvement upon Gram-Schmidt cascaded cancellers in thepresence of non-Gaussian noise outliers or equivalently, for some cases,when desired signal components are present in the training data.

[0047] A sidelobe canceller is a specific form of the general adaptivearray where the N×1 desired signal (steering) vector is set to [100 . .. 0]^(T), the “main” or first channel weight is fixed to unity, and the(N−1)×1 auxiliary channel adaptive weight vector estimate ŵ_(a)({circumflex over ( )} denotes ‘estimate of’) solves the adaptiveWiener-Hopf matrix equation,

ŵ _(a) ={circumflex over (R)} _(a) ⁻¹ {circumflex over (r)} _(am),

[0048] where {circumflex over (R)}_(a) is the (N−1)×(N−1) auxiliarychannel input noise and interference estimate, and r{circumflex over( )}_(am) is the (N−1)×1 cross-correlation vector estimate between theauxiliary channels and the main channel. For Gaussian statistics, themaximum likelihood estimates of these quantities are${\hat{R}}_{a} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}\quad {{u_{a}(k)}{u_{a}(k)}^{H}}}}$and${\hat{r}}_{am} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}\quad {{u_{a}(k)}{u_{m}(k)}^{*},}}}$

[0049] where K is the number of weight training data samples used in theaverages and * denotes complex conjugate operation. When employingequation (2) and equation (3), the sidelobe canceller uses the SMIalgorithm, and its scalar output, g, is (using vector partitioning)$g = {{w_{sic}^{H}u} = {\begin{bmatrix}1 \\\cdots \\{- {\hat{w}}_{a}}\end{bmatrix}^{H}{u.}}}$

[0050] The conventional SMI-based sidelobe canceller in this lastequation has an equivalent Gram-Schmidt cascaded canceller form in thesteady state and in the transient state with numerically identicaloutputs, where transient state refers to the case where weights areestimated from finite length data vectors. Infinite numerical accuracyis assumed, i.e., the cascaded weights correspond to a numericallyequivalent set of linear weights equation (1) that can be applieddirectly to the transformed array input data vector u via equation (4),if so desired.

[0051]FIG. 4 illustrates a conventional Gram-Schmidt canceller 20 forthe N=4 channel case, comprised of six identical two-input cancellerGram-Schmidt L₂ building blocks 22. In each building block 22, theoptimal weight estimate for that building block is calculated byminimizing the square of the L₂-norm of the residual output vector fromthat building block, over some specified number of K weight trainingdata samples.

[0052]FIG. 5 illustrates a single Gram-Schmidt L₂ building block 22. Fornotational simplicity, the left input of any single building block isrelabeled z, the right input is relabeled x, and the output is relabeledr. Each building block 22 serves to have the component of z which iscorrelated with x, subsequently subtracted from z. This is accomplishedby choosing an optimum weight estimate ŵ_(opt) such that the residual ris statistically uncorrelated with x. The least-squares method is usedto estimate w_(opt) by minimizing over the set of complex weights w, thesquare of the L₂ norm of the residual output r=z−w*x where r=r(k),z=z(k), and x=x(k), for k=1, . . . , K; i.e., for any single buildingblock,${\hat{w}}_{opt} = {{\underset{w}{\arg \quad \min}\lbrack  {\frac{1}{K}\sum\limits_{k = 1}^{K}}\quad \middle| {{z(k)} - {w^{*}{x(k)}}} |^{2} \rbrack}\quad.}$

[0053] This results in the scalar adaptive Wiener-Hopf equation,

ŵ _(opt) ={circumflex over (R)} _(xx) ⁻¹ {circumflex over (r)} _(xz),

[0054] where maximum likelihood estimates again may be used for thescalar input noise covariance estimates, assuming Gaussian statistics,${\hat{R}}_{xx} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}\quad {{x(k)}{x(k)}^{*},}}}$and${\hat{r}}_{xz} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}\quad {{x(k)}{{z(k)}^{*}.}}}}$

[0055] Note that these last two equations are sensitive to non-Gaussiannoise contaminants just like their matrix counterparts.

[0056] As set forth above the conventional general adaptive arrayprocessor may be equivalently transformed in terms of SINR into itsconventional Gram-Schmidt cascaded canceller form. The adaptiveimplementation of a conventional Gram-Schmidt cascaded cancellerprovides a cascaded set of operationally identical, two-input cancellerL₂ building blocks.

[0057] Replacing the L₂ building blocks 22 with L_(med) building blocksthroughout a cascaded canceller 30 as illustrated in FIG. 6 results inthe MMCC configuration of the present invention. FIG. 7 illustrates asingle L_(med) building block canceller 32. Each of the L_(med) buildingblocks 32 computes an adaptive weight w_(med) that in one form is acomplex adaptive weight whose real and imaginary parts are found bytaking the sample median value of the ratio of local main input weighttraining data to local auxiliary input weight training data for the realand imaginary parts separately. The preferred embodiment uses just themedian of the real parts and sets the imaginary part to zero. Each ofthe L_(med) building blocks 32 then applies the complex conjugate of thecomputed weight w*_(med) to a function of a local main input signal anda local auxiliary input signal, and generates a filtered local outputsignal, r, by solving the following equation: r=z−w*_(med)x. Althoughthe cascaded canceller illustrated has N=4 inputs, any number N ofinputs may be utilized.

[0058] In the first level of processing, N input signals are input intoN−1 L_(med) building blocks 32 to generate N−1 local output signals. Inthe next level of processing, N−1 local input signals are input into N−2L_(med) building blocks 32 to generate N−2 local output signals. Thisprocess is repeated until one final output signal remains.

[0059] The MMCC 10 of the present invention may be implemented by a setof program instructions on an arithmetical processing device such as ageneral-purpose digital signal processor (DSP) or microprocessor tocarry out in real time the computational steps presented above.Alternatively, custom-built application specific integrated circuits(ASIC), field-programmable gate arrays (FPGA), or firmware can befabricated to perform the same computations as a set of logicinstructions in hardware. These implementations are interchangeable.

[0060] The L_(med) building block 32 computes adaptive weight, w_(k), asthe sum of a real part and an imaginary part, which are found by takingthe sample median value of the ratio of local main input weight trainingdata to local auxiliary input weight training data for the real andimaginary parts separately. First, form the set w_(k) asw_(k)=(z(k)/x(k))*, for k=1,2, . . . , K where K is the number oftraining samples. The sample median of the real parts of {w_(k)} istaken as the real part of the new optimal weight, and the sample medianof the imaginary parts of {w_(k)} is taken as the imaginary part of thenew optimal weight. As K→∞, and assuming that, for this analysis, thereare no outliers, the resulting adaptive weight, $\begin{matrix}{w_{med} = {{\underset{k = {1\quad {to}\quad K}}{MED}\lbrack {{real}( \frac{{z(k)}^{*}}{{x(k)}^{*}} )} \rbrack} + {j\{ {\underset{k = {1\quad {to}\quad K}}{MED}\lbrack {{imag}( \frac{{z(k)}^{*}}{{x(k)}^{*}} )} \rbrack} \}}}} & (8)\end{matrix}$

[0061] converges to the same optimal complex weight as a Gram-Schmidt L₂building block using the same weight training data, and as shown in theabove referred to U.S. Ser. No. 09/835,127, this convergence onlyassumes symmetric densities for the real and imaginary portions of thenoise density. For Gaussian noise, the two-input convergence MOE wasshown to be E{η}=1+2/(K−1), where E denotes expectation and η denotesoutput residue power, normalized to the optimum value achievable. Thisis seen to be commensurate to the L₂ convergence MOE of 1+1/(K−1), whichis not nearly as robust as the L_(med) building block is to outliers inthe training data. The two-input L_(med) algorithm, like the two inputL₂ algorithm, convergence rate, is only a function of the number ofsamples, K, and thus is independent of the two-input, input noisecovariance matrix.

[0062] The MMCC 10 is a data-adaptive filter that can be used for signaldetection, estimation, and classification. For example, when used with asteering vector s, it can process a stream of one or more blocks of datavectors x(k) to estimate how much the data resembles a replica vector s.In more sophisticated applications, MMCC 10 can satisfy multipleconstraints (where a single steering vector s may be replaced by amatrix of steering vectors). For radar applications, these provideimproved SINR output compared to full rank methods, typically throughthe use of localized training data to improve statistical similaritywith the range cell under test (CUT).

[0063] FIGS. 8-15 demonstrate the major increase in performance obtainedfrom MMCC 10 compared with previous systems. To illustrate theperformance improvement of the MMCC over the MWF, data is modeled asreceived by an adaptive airborne (moving) radar, created using the highfidelity RLSTAP airborne radar model. There are two barrage jammers aswell as ground clutter modeled with a 45 degree antenna crab angle. TheMWF is used with a rank r=50 (out of 112 total DOF−14 antenna elementstimes 8 pulses) and K=2r=100 samples are used to train adaptive weights.The chosen steering vector points the mainbeam at zero degrees azimuthangle and at −0.47 normalized Doppler frequency.

[0064]FIG. 8(a) shows the adapted pattern produced by the MWF, after aself-normalization such that the peak pattern value is 0 dB. (Allpattern plots illustrated in these figures are self-normalized in thismanner). The simulated clutter ridge cuts diagonally across theazimuth-Doppler plane and aliases up to the limited angular extent (45deg.) of the modeled antenna pattern. There are two vertical nulls thatindicate the filter response to both barrage jammers. The target energycomes through with unity gain satisfying the MVDR constraint, howeverdue to the self-normalization, it is possible the patterns show thetarget gain different from 0 dB. The interference is well-nulled asshown by the two lines at the jammer azimuths and along the diagonalclutter ridge, but the azimuth-Doppler sidelobe levels are high, closeto the mainbeam peak level, averaging approximately −10 dB. FIG. 8(b) isa 3-dimensional view further illustrating the pattern. Therefore, anyinterference not sensed (and therefore not nulled) by the adaptivealgorithm can pass with little or no attenuation and even experiencegain, consequently masking targets or producing false alarms. Themainbeam peak is actually aliasing across both edges of the Doppler axisas seen by two peaks near −0.5 and +0.5 Doppler frequency.

[0065] For the MMCC 10, however, as shown in FIGS. 9(a) and (b), theinterference is nulled, and the average sidelobe level reduces toapproximately −25 dB, which is a 15 dB improvement compared to the MWF.This feature improves overall target detection ability when anyunder-nulled azimuth-Doppler sidelobe interference energy may be presentin the CUT. Neither extra training samples nor diagonal loading wasrequired to obtain this effect. In addition, the steering vectorsidelobes are markedly obvious for the MMCC processor, furtherillustrating the reduction in depth of the adapted azimuth-Dopplersidelobe levels.

[0066] In FIGS. 10 and 11, the MWF and MMCC patterns are shown for thesame simulated data as in FIGS. 8 and 9, except that rank r=60, andK=120 samples. There is good interference mitigation along with the sametrend of substantially lower adapted sidelobe levels. The mainbeam ispositioned near the clutter ridge (az., +0.23 Dop.) to simulate lookingfor targets at the MDV. The MMCC has a better adapted mainbeam patternin this region, indicating an improved ‘slow speed’ target detectionperformance. The MWF does not have a well-split antenna mainbeam likethe MMCC over top of the strong interference (clutter), and the MWFmainbeam peak is distorted and misaligned with the chosen steeringvector due to its proximity to, and influence by, the strong clutternull. The MMCC mainbeam resilience near strong interference is avaluable characteristic of the MMCC processor, as well as of the MCCprocessor (not illustrated).

[0067] FIGS. 12(a) and 12(b) illustrate the clutter spectrum for actualairborne radar data using a linear array at L-band. The STAP-configured,multichannel radar and data collection system used to collect the datais termed MCARM. Data was collected during a flight. For MCARM STAP dataprocessing shown here, N=11 elements and M=13 pulses were used such thatfull processor rank=143. A target of opportunity was found embedded inthe clutter data at range cell 299, approximately at 0° azimuth and+0.16 normalized Doppler frequency.

[0068] The adapted patterns formed by the MWF and MMCC processors forthe MCARM data are shown in FIGS. 13-14, respectively, for a reducedrank r=83 and using K=2r=166 samples. Both processors keep high gain onthe assumed target direction, and both null the clutter energy. However,the MMCC processor has an order 15 dB lower average adaptedazimuth-Doppler sidelobe level compared to the MWF, as seen visually inthe plot. These plots illustrate how, even with measured data, the lowsidelobe level feature of the MMCC remains intact.

[0069]FIG. 15 shows that the MCARM target of opportunity is clearlyindicated by both the MWF and the MMCC processor outputs. The range cellunder test and three guard cells on either side were excluded from theK=166 measured data training samples. Both the MWF and MMCC processorshave a peak to peak-noise level ratio (i.e., instantaneous SINR) ofapproximately 14.5 dB. However, at the same time, the MMCC adaptedazimuth-Doppler sidelobe levels are also generally significantly lessthan those of the MWF.

[0070] Accordingly, MMCC 10 exhibits significantly reduced adaptiveazimuth-Doppler sidelobe levels not characteristic of prior art devices.This significantly aids sidelobe blanking and constant false alarmfunctions.

[0071] The invention has been described with reference to certainpreferred embodiments thereof. It will be understood, however, thatmodification and variations are possible within the scope of theappended claims.

What is claimed is:
 1. In a Multistage Weiner Filter having an analysissection and a synthesis section, the filter including: a main inputchannel for receiving a main input signal; an auxiliary input channelfor receiving an auxiliary input signal; and a processor; theimprovement comprising the processor includes an algorithm forgenerating a data adaptive linear transformation followed by computingan adaptive weighting w_(med) of the data and for applying the computedadaptive weighting w_(med) to a function of the main input signal andthe auxiliary input signal to generate an output signal.
 2. A MultistageWeiner Filter as in claim 1, wherein the adaptive weighting w_(med)comprises a sample median value of the real part of the ratio of a maininput weight training data signal to an auxiliary input weight trainingdata signal, and a sample median value of the imaginary part of theratio of a main input weight training data signal to an auxiliary inputweight training data signal.
 3. A Multistage Weiner Filter as in claim1, wherein the adaptive weighting w_(med) comprises a sample medianvalue of the real part of a ratio of a main input weight training datasignal to an auxiliary input weight training data signal.
 4. AMultistage Weiner Filter as in claim 1, wherein the adaptive weightingw_(med) is obtained from the equation:$w_{med} = {{\underset{k = {1\quad {to}\quad K}}{MED}\lbrack {{real}( \frac{{z(k)}^{*}}{{x(k)}^{*}} )} \rbrack} + {j\{ {\underset{k = {1\quad {to}\quad K}}{MED}\lbrack {{imag}( \frac{{z(k)}^{*}}{{x(k)}^{*}} )} \rbrack} \}}}$

where K is the number of weight training data samples, z is the maininput signal, j is a unit imaginary number, and x is the auxiliary inputsignal.
 5. A Multistage Weiner Filter as in claim 4, wherein the outputsignal, r, is obtained from the equation: r=z−w* _(med) x.
 6. AMultistage Weiner Filter as in claim 5, wherein the processor includes areduced rank truncation to decrease training data requirements andreduce processing time.
 7. In a Multistage Weiner Filter for receiving aplurality of input signals corresponding to a common target signal andfor sequentially decorrelating the input signals to cancel thecorrelated noise components therefrom, the filter having an analysissection and a synthesis section, and the filter further including: adata adaptive linear transformation to apply to an input data vector; aplurality of building blocks arranged in a cascaded configuration forsequentially decorrelating each of the input signals from each other ofthe input signals to thereby yield a single filtered output signal;wherein each building block includes: a local main input channel whichreceives a local main input signal, a local auxiliary input channelwhich receives a local auxiliary input signal, and a processor; theimprovement comprising the processor includes an algorithm forcalculating an adaptive weighting w_(med), and generating a local outputsignal, utilizing the adaptive weighting w_(med).
 8. A Multistage WeinerFilter as in claim 7, wherein the adaptive weighting w_(med) comprises:a sample median value of the real part of the ratio of a main inputweight training data signal to an auxiliary input weight training datasignal, and a sample median value of the imaginary part of the ratio ofa main input weight training data signal to an auxiliary input weighttraining data signal..
 9. A Multistage Weiner Filter as in claim 7,wherein each building block supplies the local output signal to a localoutput channel.
 10. A Multistage Weiner Filter as in claim 7, whereinthe adaptive weighting w_(med) is obtained from the equation:$w_{med} = {{\underset{k = {1\quad {to}\quad K}}{MED}\lbrack {{real}( \frac{{z(k)}^{*}}{{x(k)}^{*}} )} \rbrack} + {j\{ {\underset{k = {1\quad {to}\quad K}}{MED}\lbrack {{imag}( \frac{{z(k)}^{*}}{{x(k)}^{*}} )} \rbrack} \}}}$

where K is the number of weight training data samples, z is the localmain input signal, j is a unit imaginary number, and x is the localauxiliary input signal; and the local output signal, r, from eachbuilding block is obtained from the equation: r=z−w* _(med) x.
 11. AMultistage Weiner Filter as in claim 10, wherein the processor includesa reduced rank truncation to decrease training data requirements andreduce processing time.
 12. An adaptive signal processing method,comprising the steps of: receiving a plurality of input signalscorresponding to a common target signal; transforming the input signalsto a data stream; applying the data stream to a steering vector tocommence processing with non-adaptive calculations by forming an initialestimate of the desired signal; isolating the rest of the data byapplying the transform x₀(k)=Bx(k), where B is a blocking matrix forfinding a projection of the data orthogonal to the steering vector;applying the initial data and the orthogonal projection of the data toat least one adaptive stage processor, said applying including:determining the projection of the data in the direction most correlatedwith the desired signal; determining the orthogonal projection to thedirection most correlated with the desired signal; applying saidprojections to the data; inputting the input signals into a plurality ofbuilding blocks arranged in a cascade configuration for sequentiallydecorrelating each of the input signals from each other of the inputsignals; in each building block, calculating an adaptive weightingw_(med) and generating a local output signal, utilizing the adaptiveweighting w_(med); and generating a single filtered output signal. 13.An adaptive signal processing method as in claim 12, wherein theadaptive weighting w_(med) from each building block is obtained bycalculating a sample median value of the real part of a ratio of a maininput weight training data signal to an auxiliary input weight trainingdata signal and calculating a sample median value of the imaginary partof the ratio of a main input weight training data signal to an auxiliaryinput weight training data signal.
 14. An adaptive signal processingmethod as in claim 12, wherein in each building block the adaptiveweighting w_(med) is obtained by calculating a sample median value ofthe real part of the ratio of a main input weight training data signalto an auxiliary input weight training data signal.
 15. An adaptivesignal processing method as in claim 12, wherein the adaptive weightingw_(med) in each building block is obtained by calculating a samplemedian value of the imaginary part of a ratio of a main input weighttraining data signal to an auxiliary input weight training data signal.16. An adaptive signal processing method as claimed in claim 12, whereinthe adaptive weighting w_(med) in each building block is obtained fromthe equation:$w_{med} = {{\underset{k = {1\quad {to}\quad K}}{MED}\lbrack {{real}( \frac{{z(k)}^{*}}{{x(k)}^{*}} )} \rbrack} + {j\{ {\underset{k = {1\quad {to}\quad K}}{MED}\lbrack {{imag}( \frac{{z(k)}^{*}}{{x(k)}^{*}} )} \rbrack} \}}}$

where K is the number of weight training data samples, z is the localmain input signal, j is the unit imaginary vector, and x is the localauxiliary input signal.
 17. An adaptive signal processing method asclaimed in claim 16, wherein the local output signal, r, in eachbuilding block is obtained from the equation: r=z−w* _(med) x.
 18. Anadaptive signal processing method as claimed in claim 17, wherein theprocessor includes a reduced rank truncation to decrease training datarequirements and reduce processing time.
 19. A multistage mediancascaded canceller, comprising: a means for receiving a plurality ofinput signals corresponding to the same target signal; a means fortransforming the input signals to a data stream; a means for applyingthe data stream to a steering vector to commence processing withnon-adaptive calculations by forming an initial estimate of the desiredsignal; a means for isolating the rest of the data by applying thetransform x₀(k)=Bx(k), where B is a blocking matrix for finding aprojection of the data orthogonal to the steering vector; a means ofdetermining and applying a data adaptive linear transformation via acascade of orthogonal subspace projections to create an efficient inputdata transformation; a means for applying the initial data and theorthogonal projection of the data to at least one adaptive stageprocessor, said adaptive stage processor including a plurality ofbuilding blocks arranged in a cascade configuration for sequentiallydecorrelating each of the input signals from each other of the inputsignals; and a means for generating a single filtered output signal; andwherein each building block includes a means for receiving a local maininput signal, a means for receiving a local auxiliary input signal, anda processing means for calculating an adaptive weighting w_(med), andgenerating a local output signal, utilizing the adaptive weightingw_(med).
 20. A multistage median cascaded canceller as in claim 19,wherein the adaptive weighting w_(med) comprises: a sample median valueof the real part of a ratio of a main input weight training data signalto an auxiliary input weight training data signal, and a sample medianvalue of the imaginary part of the ratio of a main input weight trainingdata signal to an auxiliary input weight training data signal.
 21. Amultistage median cascaded canceller as in claim 19, wherein theadaptive weighting w_(med) comprises a sample median value of the realpart of a ratio of a main input weight training data signal to anauxiliary input weight training data signal.
 22. A multistage mediancascaded canceller as in claim 19, wherein the adaptive weightingw_(med) in each building block is obtained from the equation:$w_{med} = {{\underset{k = {1\quad {to}\quad K}}{MED}\lbrack {{real}( \frac{{z(k)}^{*}}{{x(k)}^{*}} )} \rbrack} + {j\{ {\underset{k = {1\quad {to}\quad K}}{MED}\lbrack {{imag}( \frac{{z(k)}^{*}}{{x(k)}^{*}} )} \rbrack} \}}}$

where K is the number of weight training data samples, z is the localmain input signal, j is the unit imaginary vector, and x is the localauxiliary input signal; and generates the local output signal, r, bysolving the equation: r=z−w* _(med) x.
 23. A multistage median cascadedcanceller as in claim 22, wherein the processor includes a reduced ranktruncation to decrease training data requirements and reduce processingtime.
 24. A multistage median cascaded canceller for receiving aplurality input signals corresponding to a common target signal and forsequentially decorrelating the input signals to cancel the correlatednoise components therefrom, comprising: an analysis section; a synthesissection; a processor configured for: applying the data stream to asteering vector to commence processing with non-adaptive calculations byforming an initial estimate of the desired signal; isolating the rest ofthe data by applying the transform x₀(k)=Bx(k), where B is a blockingmatrix for finding a projection of the data orthogonal to the steeringvector; applying the initial data and the orthogonal projection of thedata to at least one adaptive stage processor, said adaptive stageprocessor including a plurality of building blocks arranged in a cascadeconfiguration having N input channels and N−1 rows of building blocks,for sequentially decorrelating each of the input signals from each otherof the input signals to thereby yield a single filtered output signal;wherein each building block includes: a local main input channel whichreceives a local main input signal, a local auxiliary input channelwhich receives a local auxiliary input signal, and wherein the processoris further configured to calculate an adaptive weighting w_(med) andgenerate a local output signal, utilizing the adaptive weightingw_(med); and wherein an end building block supplies the local outputsignal to a separate local output channel for follow on processing. 25.A multistage median cascaded canceller as in claim 24, wherein the Nthinput channel is supplied for follow on processing.
 26. A multistagemedian cascaded canceller as in claim 24, wherein said adaptiveweighting w_(med) comprises: a sample median value of the real part of aratio of a main input weight training data signal to an auxiliary inputweight training data signal, and a sample median value of the imaginarypart of the ratio of a main input weight training data signal to anauxiliary input weight training data signal.
 27. A multistage mediancascaded canceller as in claim 24, wherein said adaptive weightingw_(med) comprises a sample median value of the real part of a ratio of amain input weight training data signal to an auxiliary input weighttraining data signal.
 28. A multistage median cascaded canceller as inclaim 24, wherein said adaptive weighting w_(med) is obtained from theequation:$w_{med} = {{\underset{k = {1\quad {to}\quad K}}{MED}\lbrack {{real}( \frac{{z(k)}^{*}}{{x(k)}^{*}} )} \rbrack} + {j\{ {\underset{k = {1\quad {to}\quad K}}{MED}\lbrack {{imag}( \frac{{z(k)}^{*}}{{x(k)}^{*}} )} \rbrack} \} {\quad,}}}$

where K is the number of weight training data samples, z is the localmain input signal, j is the unit imaginary vector, and x is the localauxiliary input signal; and the local output signal r is obtained fromthe equation: r=z−w* _(med) x.
 29. A multistage median cascadedcanceller as in claim 28, wherein the processor includes a reduced ranktruncation to decrease training data requirements and reduce processingtime.